MATHEMATICS (TURKISH, PHD) | |||||
PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
MAT5017 | Probability | Fall | 3 | 0 | 3 | 12 |
The course opens with the approval of the Department at the beginning of each semester |
Language of instruction: | Tr |
Type of course: | Departmental Elective |
Course Level: | |
Mode of Delivery: | Face to face |
Course Coordinator : | Dr. GENCO FAS |
Course Objectives: | The course will provide an introduction to stochastic processes for whose applications in engineering, managerial sciences and service sector are described. M |
The students who have succeeded in this course; Students will be learned stochastic modelling and processes |
Markov chains and Poisson Processes follow a brief review of fundamentals of probability. Besides; renewal, regenerative and queueing processes are mentioned. Inventory control and finance are two additonal topics to the course. |
Week | Subject | Related Preparation | |
1) | Introduction: Fundamental concepts of probability | ||
2) | Some Basic Discrete and Continuous Distributions | ||
3) | Introduction to Stochastic Processes, Definitions, Conditional Expectation and Variance. | ||
4) | Branching Processes | ||
5) | Two-dimensional Random Walk and Bernoulli Processes | ||
6) | Discrete-time Markov Chains (Definitions, Classifications, Transition Matrix) | ||
7) | Limiting and Stationary Distributions | ||
8) | Exponential Distribution | ||
9) | Poisson Processes | ||
10) | Continuous-time Markov Chains | ||
11) | Limiting Probabilities, Hitting Probabilities and Times | ||
12) | Queueing Theory | ||
13) | Little's Law and Applications | ||
14) | Introduction to Brownian Motion |
Course Notes: | Introduction to Probability Models, Sheldon Ross, Academic Press, 9th Edition |
References: | Probability and Statistics for Engineers and Scientists, Walpole, Myers, Myers, Ye, Prentice Hall, 8th edition. Introduction to Probability, Bertsekas, Tsitliklis |
Semester Requirements | Number of Activities | Level of Contribution |
Attendance | 14 | % 10 |
Laboratory | % 0 | |
Application | % 0 | |
Field Work | % 0 | |
Special Course Internship (Work Placement) | % 0 | |
Quizzes | 2 | % 10 |
Homework Assignments | 2 | % 10 |
Presentation | % 0 | |
Project | % 0 | |
Seminar | % 0 | |
Midterms | 1 | % 30 |
Preliminary Jury | % 0 | |
Final | 1 | % 40 |
Paper Submission | % 0 | |
Jury | % 0 | |
Bütünleme | % 0 | |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 60 | |
PERCENTAGE OF FINAL WORK | % 40 | |
Total | % 100 |
Activities | Number of Activities | Duration (Hours) | Workload |
Course Hours | 14 | 3 | 42 |
Laboratory | 0 | 0 | 0 |
Application | 0 | 0 | 0 |
Special Course Internship (Work Placement) | 0 | 0 | 0 |
Field Work | 0 | 0 | 0 |
Study Hours Out of Class | 14 | 9 | 126 |
Presentations / Seminar | 2 | 2 | 4 |
Project | 0 | 0 | 0 |
Homework Assignments | 3 | 8 | 24 |
Quizzes | 0 | 0 | 0 |
Preliminary Jury | 0 | ||
Midterms | 1 | 2 | 2 |
Paper Submission | 0 | ||
Jury | 0 | ||
Final | 1 | 2 | 2 |
Total Workload | 200 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution |